Gamma spectrometry is commonly used to detect the presence of radio activity in environmental samples. With the large amount of decontamination and decommissioning work expected to be performed in the US as well as overseas, the number of such measurements is likely to increase significantly in the near future. The current gamma spectrometry practices have two shortcomings. The normal practice of calibration requires a calibration standard carefully manufactured to be identical to each sample size and shape, or as nearly so as possible. With many different sizes, shapes, and chemical compositions of samples, such a calibration can be both time consuming and expensive. The second problem is that, due to the low activities involved, it is customary to bring the sample as close to the detector as possible to increase the sensitivity of analysis and/or to reduce the measurement times. This gives rise to often significant amount of coincidence summing (also called cascade summing). Current commercial software codes, and nearly all research codes, are not able to correct for this effect in the reported results, even though the required correction factors are often more than 10% and sometimes as high as 50%.
With voluminous sources, such as the samples commonly used with close measurement geometries, the parts of the sample that are close to the detector exhibit more cascade summing effects than the parts that are further away from the detector. For such cases, the overall correction is a combination of rather large correction factors and rather small correction factors.
The majority of radionuclides decay by emitting multiple gamma- and X-ray photons in cascades with negligible time delay (at least in less time than the resolution time of detector systems). In the detector crystal, this causes energy depositions which are impossible to attribute to the proper emission energy (nuclear level transition) and the detector system is thus able to register only a summing effect. This true coincidence effect causes summing in or summing out. Summing in leads to an increase of an observable peak area, whereas summing out leads to a decrease of an observable peak area. The total effect with respect to a gamma-line `g` of a radionuclide under consideration is: EQU CO1.sub.g =(1-Lg)(1+Sg)
where Lg is the probability of summing out and Sg is the probability of summing in. The corrected peak area (N'.sub.p,g) is computed from the observable peak area (N.sub.p,g) using the equation: ##EQU2##
The general quantitative procedure for treatment of true coincidence effect in the case of complex decay schemes has been considered by Andreev et al. (1. D. S. Andreev, et al. Instr. Expt. Techn., 15 (1972) p.1358 and D. S. Andreev, et al., Izv. Akad. Nauk SSSR, Ser. Fiz., 37 (1973), N.8, p.1609). Verplancke (J. C. Verplancke, Nucl. Instr. Meth. Phys. Res., 96 (1971), p.557.) proposed a formula for estimation of efficiency in the case of coincidence summing for .sup.60 Co and .sup.88 Y, and has considered positron-gamma cascades. McCallum and Coote (G. J. McCallum and G. E. Coote, Nucl. Instr. Meth. Phys. Res., 130 (1975), p.189.) considered the case of gamma-beta+ coincidence summing out and demonstrated the workability of their approach for 22Na. Gehrke et al. (R. J. Gehrke, et al., Nucl. Instr. Meth. Phys. Res., 147 (1977), p.405.) tabulated the coincidence summing corrections for some radionuclides measured with a Ge(Li) detector at 10-cm distance. Debertin and Schotzig (K. Debertin and U. Schotzig, Nucl. Instr. Meth. Phys. Res., 158 (1979) p.471.) experimentally checked Andreev's solution for .sup.60 Co, .sup.88 Y, and .sup.152 Eu for point and beaker geometries close to the detector. Moens (L. Moens, Doctorate Thesis, Rijksuniversiteit, Gent (1981) and L.Moens, et al., J. Radioanal. Chem. 70 (1982), p. 539.) generalized the method, suggested the use of gamma intensities instead of beta intensities, and derived mathematical formulae for practically important cases. De Corte (F. De Corte, Doctorate-Thesis, Rijksuniversiteit, Gent (1987)) updated the approach by Moens, and extended it for the cases of gamma-KX(EC) and gamma-KX(IT) coincidences. Jovanovich et al. (S. Jovanovic, et al., Vest. Slov. Kem. Drus., 35 (1988), N.4, p.409) discussed some practical aspects of true coincidence correction in the case of neutron activation analysis using the K.sub.0 -method. Dobreva et al.(E. Dobreva, et al., Bulg. J. Phys., 16 (1989), N.2, p.194) investigated the application of attenuators made from different materials to reduce the contribution of true-coincidence effect. Lin Xilei and Heydorn (Lin Xilei and K. Heydorn, J. Radioanal. Nucl. Chem., Articles, 169, N.2 (1993), p.419) demonstrated that application of absorbers may reduce the contribution of KX-gamma coincidences in the case of measurements with N-type detectors. De Corte and Freitas (F. De Corte and C. Freitas, J. Radioanal. Nucl. Chem., Articles, 160 (1992), p.253 and C. Freitas, et al., Biological Trace Element Research (1990), p.33) extended the method for computation of true-coincidence corrections for the case of gamma-KX coincidence. Blaauw (M. Blaauw, Nucl. Instrum. Meth. Phys. Res., A332 (1993), p.493) suggested to use artificial summing peaks for simultaneous computation of the true coincidence effect and activity in the case of point source. De Corte, et. al. (F. De Corte, et al., Nucl. Instrum. Meth. Phys. Res., A353 (1994), p.539) developed a method for estimation of true coincidence effect for the case of auger hole counting geometry ("infinite" Marinelli beaker).
This analysis of the literature shows that the problem of coincidence correction for point sources is practically resolved. However, this does not mean that the problem has been resolved for a more general case such as voluminous sources, especially those that are symmetric around the axis of the detector.
Accordingly, it is a principal object of the present invention to provide a method for characterizing radiation detectors that does not require manufacturing calibration standards nearly identical to sample sizes, shapes, chemical compositions, and/or radionuclides content.
It is a further object of the invention to provide a method for correcting for coincidence summing.
It is another object of the invention to provide such method to calibrate and correct for the coincidence summing effects in both small and voluminous radioactive samples.
It is an additional object of the invention to provide such method that is easily implemented and is accurate.
It is yet a further object of the invention to provide such method that is applicable for samples of various geometrical shapes, physical states, and chemical compositions.
It is yet another object of the invention to provide such method that is suitable for routine laboratory radioassay.
It is yet and additional object of the invention to provide such method for correcting for coincidence summing in gamma spectrometry for any radiation source that is symmetric around the axis of the detector.
Other objects of the present invention, as well as particular features, elements, and advantages thereof, will be elucidated in, or be apparent from, the following description.